Subgroups — #37563753

Order 24180.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#11925881	C₂	1	1	yes	maximal, characteristic
2	C₁₃×Dic₁₅₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×#11925881	C₄	1	1	yes	characteristic, complemented, Hall
4	#18012812	—	5	1	no	maximal, Hall
5	C₂×C₅×C₁₃×C₃₁	C₂×C₃	1	1	yes	characteristic
6	C₂×#11925881	D₅	1	1	yes	characteristic
7	C₅×C₁₃×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	(C₃₁⋊C₃)⋊Dic₅	—	13	1	no	maximal, Hall
9	C₁₃×Dic₃₁	—	5	1	no	Hall
10	#11925881	Dic₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×C₃₁⋊C₃	—	13	1	no	—
12	C₂×C₁₃×C₃₁	C₃×D₅	1	1	yes	characteristic
13	Dic₅×C₁₃⋊C₃	—	31	1	no	maximal, Hall
14	Dic₁₅₅	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₅×C₃₁⋊C₃	—	13	1	no	Hall
16	C₁₃×C₃₁	C₃×Dic₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₁₃⋊C₃	—	62	1	no	—
18	(C₃₁⋊C₃)⋊C₄	—	65	1	no	Hall
19	C₂×C₅×C₃₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic
20	C₁₃×Dic₅	—	31	1	no	Hall
21	C₅×C₁₃⋊C₃	—	62	1	no	Hall
22	C₂×C₃₁⋊C₃	—	13	1	no	—
23	C₄×C₁₃⋊C₃	—	155	1	no	Hall
24	C₅×C₃₁	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₅×C₁₃	D₃₁⋊C₃	1	1	yes	characteristic
26	Dic₃₁	—	5	1	no	Hall
27	C₃₁⋊C₃	—	13	1	no	Hall
28	C₂×C₁₃⋊C₃	—	62	1	no	—
29	C₅×C₁₃	(C₃₁⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃₁	D₅×C₁₃⋊C₃	1	1	yes	characteristic
31	C₃×Dic₅	—	403	1	no	Hall
32	C₄×C₁₃	—	155	1	no	Hall
33	C₁₃⋊C₃	—	62	1	no	Hall
34	C₃₁	Dic₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃×C₅	—	806	1	no	—
36	C₂×C₁₃	C₅⋊(D₃₁⋊C₃)	1	1	yes	characteristic
37	Dic₅	—	31	1	no	Hall
38	C₃×C₅	—	806	1	no	Hall
39	C₁₃	(C₃₁⋊C₃)⋊Dic₅	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	2015	1	no	Hall
41	C₂×C₅	#14559023	1	1	yes	characteristic
42	C₂×C₃	—	806	1	no	—
43	C₅	#18012812	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	155	1	no	Sylow
45	C₃	—	806	1	no	Sylow
46	C₂	C₅⋊#14559023	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅⋊#14559023
commutator, hypocenter	C₅×C₁₃×C₃₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₅×C₁₃×C₃₁	C₂×C₃
prime radical	C₂×C₅×#11925881	C₂
LCS	G ▷ C₅×C₁₃×C₃₁
UCS	C₁ ◁ C₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₃×Dic₁₅₅	C₃	semidirect
3. C₅×#11925881	C₄	semidirect
7. C₅×C₁₃×C₃₁	C₃×C₄	semidirect
10. #11925881	Dic₅	semidirect
14. Dic₁₅₅	C₁₃⋊C₃	semidirect
16. C₁₃×C₃₁	C₃×Dic₅	semidirect
24. C₅×C₃₁	C₄×C₁₃⋊C₃	semidirect
29. C₅×C₁₃	(C₃₁⋊C₃)⋊C₄	semidirect
34. C₃₁	Dic₅×C₁₃⋊C₃	semidirect
39. C₁₃	(C₃₁⋊C₃)⋊Dic₅	semidirect
43. C₅	#18012812	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×#11925881	2
C₁₃×Dic₁₅₅	3
#18012812	5
(C₃₁⋊C₃)⋊Dic₅	13
Dic₅×C₁₃⋊C₃	31